EAP

Release 1.1.14.1

This package is designed for empirical asset pricing

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License
MIT
Install
pip install EAP==1.1.14.1

Documentation

EAP

empirical asset pricing

Documentation

Module

portfolio_analysis

This package is used for portfolio analysis including 4 steps:

  1. select breakpoints
  2. distribute the assets into groups
  3. calculate the average and difference of groups
  4. present the result

class ptf_analysis()

This class is for portfolio analysis containing few functions.

def select_breakpoints(self, character, number, perc=None):

This function, corresponding to the step 1, selects the breakpoints of the sample.

**input : **

character : The asset characteristic by which the assets are grouped.

number : The number of the breakpoint and the number of interval is number+1. Once the number is given, the assets would be grouped into number+1 groups by the average partition of the asset characteristic.

perc : That perc is a list of number, represents the percentiles of the characteristic by which group the assets. Once it is set, then number is invalid.

output :

breakpoint : The breakpoint is the percentiles of the asset characteristic, ranging from 0% to 100%, whose in length is number+2.

Example

from EAP.portfolio_analysis import Ptf_analysis as ptfa
import matplotlib.pyplot as plt
import numpy as np

# generate characteristics
character = np.random.normal(0, 100, 10000)
# generate breakpoint
breakpoint = ptfa().slect_breakpoint(character=character, number=9)
print('Breakpoint:', breakpoint)
# comapre with the true breakpoint
for i in np.linspace(0, 100, 11):
        print('True breakpoint', i, '%:', np.percentile(character,i))

========================================================================
Generated breakpoint: [-418.25352494 -127.85494153  -84.90868131  -53.27163604  -25.2394311   1.74938872   25.93867426   50.87047751   84.42711213  128.52009426  334.42181608]
True breakpoint 0.0 %: -418.25352493659074
True breakpoint 10.0 %: -127.85494153240666
True breakpoint 20.0 %: -84.90868130631613
True breakpoint 30.0 %: -53.271636036097135
True breakpoint 40.0 %: -25.239431099072657
True breakpoint 50.0 %: 1.7493887248228535
True breakpoint 60.0 %: 25.938674261710755
True breakpoint 70.0 %: 50.870477505977846
True breakpoint 80.0 %: 84.42711212754239
True breakpoint 90.0 %: 128.5200942602427
True breakpoint 100.0 %: 334.42181607589504
========================================================================
def distribute(self, character, breakpoint):

This function, corresponding to the step 2, distributes the assets into groups by characteristics grouped by the breakpoint.

input :

character : The characteristic by which the assets are grouped.

breakpoint : The breakpoint of the characteristic.

**output : **

label : an array containing the group number of each asset.

Example

# continue the previous code
# generate the groups     
print('The Label of unique value:\n', np.sort(np.unique(ptfa().distribute(character, breakpoint))))
# plot the histogram of the label 
# each group have the same number of samples
plt.hist(ptfa().distribute(character, breakpoint))
label = ptfa().distribute(character, breakpoint)[:, 0]
# print the label
print('Label:\n', ptfa().distribute(character, breakpoint))
========================================================================
The Label of unique value:
 [0. 1. 2. 3. 4. 5. 6. 7. 8. 9.]
Label:
 [[2.]
 [8.]
 [1.]
 ...
 [1.]
 [4.]
 [8.]]
def average(self, sample_return, label):

This function, corresponding to the step 3, calculates the average return for each group.

input :

sample_return : The return of each asset

label : The group label of each asset

output :

average_return : The average return of each group

Example

# continue the previous code
# generate the future sample return
sample_return = character/100 + np.random.normal()
ave_ret = ptfa().average(sample_return, label)
# print the groups return
print('average return for groups:\n', ave_ret)
========================================================================
average return for groups:
 [[-1.47855293]
 [-0.75343815]
 [-0.39540537]
 [-0.0971466 ]
 [ 0.17474793]
 [ 0.42303036]
 [ 0.68905747]
 [ 0.95962212]
 [ 1.33445632]
 [ 2.03728439]]

class Univariate(ptf_analysis):

This class is designed for univariate portfolio analysis.

def _init_ (self, sample, number, perc=None, factor=None, maxlag=12):

The initialization function

input :

sample : The samples to be analyzed. Samples usually contain the future return, characteristics, time. The DEFAULT setting is the 1th column is the forecast return, the 2nd column is the characteristic, the 3rd column or the index(if data type is Dataframe) is time label.

number : The breakpoint number.

perc : The breakpoint percentiles.

factor : The risk factor used to adjust the asset return.

maxlag : The maximum lag for Newey-West adjustment.

def divide_by_time(self):

This function groups the sample by time.

output :

groups_by_time : The samples group by time.

def average_by_time(self):

This function, using the sample group by time from function divide_by_time, groups the sample by the characteristic, and then calculate average return of each group samples at every time point.

output :

average_group_time(matrix: N_T) : The average return of groups by each characteristic-time pair.

Example

import numpy as np
from portfolio_analysis import Univariate as uni
    
# generate time 
year=np.ones((3000,1),dtype=int)*2020
for i in range(19):
    year=np.append(year,(2019-i)*np.ones((3000,1),dtype=int))
    
# generate character
character=np.random.normal(0,1,20*3000)
# generate future return
ret=character*-0.5+np.random.normal(0,1,20*3000)
# create sample containing future return, character, time
sample=np.array([ret,character,year]).T
# initializ the univariate object
exper=uni(sample,9)
# 
data=exper.average_by_time()
print(data)
==========================================================================================================================
[[ 0.82812256  0.87549215  0.81043114  0.77480366  0.85232487  0.85599445   0.90860961  0.76600211  0.91360546  0.85921985  0.96717798  0.77677131   0.88669273  0.86895145  0.97832435  0.88494486  0.82571951  0.84777939   0.89373487  0.95906454]
 [ 0.51155724  0.4963439   0.6100762   0.47351625  0.46844971  0.53303287   0.52087477  0.43934316  0.51169633  0.61918844  0.56254028  0.50949226   0.39033219  0.49685445  0.5844816   0.48723354  0.49861094  0.43197525   0.40040156  0.57529228]
 [ 0.41566251  0.3421546   0.27117215  0.35550346  0.28884636  0.43710998   0.33146264  0.27860032  0.35956881  0.34818479  0.35692361  0.42462374   0.16909231  0.33823117  0.31762348  0.44863438  0.42785283  0.20093775   0.29664738  0.31509963]
 [ 0.21972246  0.24685649  0.29933776  0.09880866  0.13564638  0.17673649   0.14251437  0.12188551  0.1567432   0.20428427  0.15009782  0.08488247   0.20489871  0.10598241  0.12591301  0.17287433  0.11180376  0.09941738   0.22635281  0.22828588]
 [ 0.01851548  0.05771421  0.0624163   0.05368921  0.15247324  0.05839522   0.05864669  0.01863668 -0.08367879  0.09273579  0.18374921  0.12331214   0.03635538  0.05804576  0.0116589  -0.04158565  0.11655945  0.09727234   0.14038867  0.13594649]
 [-0.07910789 -0.04670755  0.08732773 -0.07361966 -0.00232509 -0.08546681  -0.15020487 -0.05302521 -0.07922696 -0.1088824  -0.01700017 -0.06742183   0.00190131  0.00961174 -0.05953252 -0.09504501 -0.0958816  -0.00355493  -0.08553405 -0.05343558]
 [-0.13094033 -0.23888179 -0.11046595 -0.11176528 -0.14017103 -0.17184142  -0.26587781 -0.14426219 -0.15687278 -0.15962335 -0.18586504 -0.2367552  -0.26761165 -0.16169935 -0.26608677 -0.16202763 -0.24272797 -0.17049684  -0.21470737 -0.13520545]
 [-0.35621842 -0.28111488 -0.42057927 -0.37219582 -0.25449753 -0.36362452  -0.34165952 -0.28564624 -0.29936621 -0.32545156 -0.28208242 -0.36730096  -0.24269836 -0.31584032 -0.34207757 -0.35185102 -0.35515763 -0.32239715  -0.2803911  -0.36334961]
 [-0.58529295 -0.54329245 -0.52006031 -0.49856708 -0.44262707 -0.4464171  -0.58846501 -0.56725297 -0.35845646 -0.52923391 -0.42119445 -0.55659388  -0.47716067 -0.4574991  -0.52123094 -0.54767832 -0.50289813 -0.45529132  -0.58429513 -0.48110405]
 [-0.81992395 -0.95766159 -0.92069685 -0.92906348 -0.84891875 -0.81670916  -0.90281776 -0.84845902 -0.90479169 -0.86860559 -0.96790821 -0.9464988  -0.88176205 -0.96118242 -0.92402295 -0.81623283 -0.81560442 -0.85841478  -0.87337267 -0.8070857 ]]
def difference(self, average_group):

This functions calculates the difference of group return, which, in detail, is the last group average return minus the first group average return.

input :

average_group : The average return of groups by each characteristic-time pair.

output :

result : The matrix added with the difference of average group return.

def factor_adjustment(self, result):

This function calculates the group return adjusted by risk factors.

input :

result : The return table with difference sequence.

output :

alpha : The anomaly

ttest : The t-value of the anomaly.

def summary_and_test(self):

This function summarizes the result and take t-test.

**output : **

self.average :

self.ttest :

def print_summary_by_time(self):

This function print the summary grouped by time.

def print_summary(self):

This function print the summary grouped by characteristic and averaged by time.

Example

# continue the previous code
exper.summary_and_test()
exper.print_summary_by_time()
========================================================================================================
+--------+-------+-------+-------+-------+--------+--------+--------+--------+--------+--------+--------+
|  Time  |   1   |   2   |   3   |   4   |   5    |   6    |   7    |   8    |   9    |   10   |  diff  |
+--------+-------+-------+-------+-------+--------+--------+--------+--------+--------+--------+--------+
| 2001.0 | 0.828 | 0.512 | 0.416 |  0.22 | 0.019  | -0.079 | -0.131 | -0.356 | -0.585 | -0.82  | -1.648 |
| 2002.0 | 0.875 | 0.496 | 0.342 | 0.247 | 0.058  | -0.047 | -0.239 | -0.281 | -0.543 | -0.958 | -1.833 |
| 2003.0 |  0.81 |  0.61 | 0.271 | 0.299 | 0.062  | 0.087  | -0.11  | -0.421 | -0.52  | -0.921 | -1.731 |
| 2004.0 | 0.775 | 0.474 | 0.356 | 0.099 | 0.054  | -0.074 | -0.112 | -0.372 | -0.499 | -0.929 | -1.704 |
| 2005.0 | 0.852 | 0.468 | 0.289 | 0.136 | 0.152  | -0.002 | -0.14  | -0.254 | -0.443 | -0.849 | -1.701 |
| 2006.0 | 0.856 | 0.533 | 0.437 | 0.177 | 0.058  | -0.085 | -0.172 | -0.364 | -0.446 | -0.817 | -1.673 |
| 2007.0 | 0.909 | 0.521 | 0.331 | 0.143 | 0.059  | -0.15  | -0.266 | -0.342 | -0.588 | -0.903 | -1.811 |
| 2008.0 | 0.766 | 0.439 | 0.279 | 0.122 | 0.019  | -0.053 | -0.144 | -0.286 | -0.567 | -0.848 | -1.614 |
| 2009.0 | 0.914 | 0.512 |  0.36 | 0.157 | -0.084 | -0.079 | -0.157 | -0.299 | -0.358 | -0.905 | -1.818 |
| 2010.0 | 0.859 | 0.619 | 0.348 | 0.204 | 0.093  | -0.109 | -0.16  | -0.325 | -0.529 | -0.869 | -1.728 |
| 2011.0 | 0.967 | 0.563 | 0.357 |  0.15 | 0.184  | -0.017 | -0.186 | -0.282 | -0.421 | -0.968 | -1.935 |
| 2012.0 | 0.777 | 0.509 | 0.425 | 0.085 | 0.123  | -0.067 | -0.237 | -0.367 | -0.557 | -0.946 | -1.723 |
| 2013.0 | 0.887 |  0.39 | 0.169 | 0.205 | 0.036  | 0.002  | -0.268 | -0.243 | -0.477 | -0.882 | -1.768 |
| 2014.0 | 0.869 | 0.497 | 0.338 | 0.106 | 0.058  |  0.01  | -0.162 | -0.316 | -0.457 | -0.961 | -1.83  |
| 2015.0 | 0.978 | 0.584 | 0.318 | 0.126 | 0.012  | -0.06  | -0.266 | -0.342 | -0.521 | -0.924 | -1.902 |
| 2016.0 | 0.885 | 0.487 | 0.449 | 0.173 | -0.042 | -0.095 | -0.162 | -0.352 | -0.548 | -0.816 | -1.701 |
| 2017.0 | 0.826 | 0.499 | 0.428 | 0.112 | 0.117  | -0.096 | -0.243 | -0.355 | -0.503 | -0.816 | -1.641 |
| 2018.0 | 0.848 | 0.432 | 0.201 | 0.099 | 0.097  | -0.004 | -0.17  | -0.322 | -0.455 | -0.858 | -1.706 |
| 2019.0 | 0.894 |  0.4  | 0.297 | 0.226 |  0.14  | -0.086 | -0.215 | -0.28  | -0.584 | -0.873 | -1.767 |
| 2020.0 | 0.959 | 0.575 | 0.315 | 0.228 | 0.136  | -0.053 | -0.135 | -0.363 | -0.481 | -0.807 | -1.766 |
+--------+-------+-------+-------+-------+--------+--------+--------+--------+--------+--------+--------+

exper.print_summary()
==================================================================================================================
+---------+--------+--------+--------+--------+-------+--------+---------+---------+---------+---------+---------+
|  Group  |   1    |   2    |   3    |   4    |   5   |   6    |    7    |    8    |    9    |    10   |   Diff  |
+---------+--------+--------+--------+--------+-------+--------+---------+---------+---------+---------+---------+
| Average | 0.867  | 0.506  | 0.336  | 0.166  | 0.068 | -0.053 |  -0.184 |  -0.326 |  -0.504 |  -0.883 |  -1.75  |
|  T-Test | 63.706 | 35.707 | 20.199 | 12.637 |  4.6  | -4.463 | -15.616 | -32.172 | -36.497 | -73.162 | -92.152 |
+---------+--------+--------+--------+--------+-------+--------+---------+---------+---------+---------+---------+

# generate factor
factor=np.random.normal(0,1.0,(20,1))
exper=uni(sample,9,factor=factor,maxlag=12)
# print(exper.summary_and_test()) # if needed
exper.print_summary()
====================================================================================================================
+---------+--------+--------+--------+--------+-------+---------+---------+---------+---------+---------+----------+
|  Group  |   1    |   2    |   3    |   4    |   5   |    6    |    7    |    8    |    9    |    10   |   Diff   |
+---------+--------+--------+--------+--------+-------+---------+---------+---------+---------+---------+----------+
| Average | 0.867  | 0.506  | 0.336  | 0.166  | 0.068 |  -0.053 |  -0.184 |  -0.326 |  -0.504 |  -0.883 |  -1.75   |
|  T-Test | 63.706 | 35.707 | 20.199 | 12.637 |  4.6  |  -4.463 | -15.616 | -32.172 | -36.497 | -73.162 | -92.152  |
|  Alpha  | 0.869  | 0.507  | 0.336  | 0.164  | 0.067 |  -0.054 |  -0.184 |  -0.326 |  -0.503 |  -0.883 |  -1.752  |
| Alpha-T | 62.39  | 69.24  | 43.377 | 16.673 | 8.204 | -12.372 | -16.679 | -65.704 | -87.618 | -93.223 | -139.881 |
+---------+--------+--------+--------+--------+-------+---------+---------+---------+---------+---------+----------+

fama_macbeth

This module is designed for Fama_Macbeth regression(1976).

Fama-Macbeth Regression follows two steps:

  1. Specify the model and take cross-sectional regression.
  2. Take the time-series average of regression coefficient

For more details, please read Empirical Asset Pricing: The Cross Section of Stock Returns. Bali, Engle, Murray, 2016.

class Fama_macbeth_regress():

Package Needed: numpy, statsmodels, scipy, prettytable.

def _init_(self, sample):

input :

sample : data for analysis. The structure of the sample :

​ The first column is dependent variable/ test portfolio return.

​ The second to the last-1 columns are independent variable/ factor loadings.

​ The last column is the time label.

def divide_by_time(self, sample):

This function group the sample by time.

input :

sample : The data for analysis in the _init_ function.

output :

groups_by_time : The sample grouped by time.

def cross_sectional_regress(self, add_constant=True):

This function conducts the first step of Fama-Macebth Regression Fama-Macbeth, that taking the cross-sectional regression for each period.

input :

add_constant : whether add intercept when take the cross-sectional regression

output :

parameters : The regression coefficient/factor risk premium, whose rows are the group coefficient and columns are regression variable.

tvalue : t value for the coefficient.

rsquare : The r-square.

adjrsq : The adjust r-square.

n : The sample quantity in each group.

def time_series_average(self, **kwargs):

This function conducts the second step of Fama-Macbeth regression, take the time series average of cross section regression.

def fit(self, **kwargs):

This function fits the model by running the time_series_average function.

Example

import numpy as np
from fama_macbeth import Fama_macbeth_regress
    
# construct sample
year=np.ones((3000,1),dtype=int)*2020
for i in range(19):
    year=np.append(year,(2019-i)*np.ones((3000,1),dtype=int))
character=np.random.normal(0,1,(2,20*3000))
# print('Character:',character)
ret=np.array([-0.5,-1]).dot(character)+np.random.normal(0,1,20*3000)
sample=np.array([ret,character[0],character[1],year]).T    
# print('Sample:',sample)
# print(sample.shape)

model = Fama_macbeth_regress(sample)
result = model.fit(add_constant=False)
print(result)
=========================================================================
para_average: [-0.501 -1.003]
tvalue: [-111.857 -202.247]
R: 0.5579113793318332
ADJ_R: 0.5576164569698131
sample number N: 3000.0
def summary_by_time(self):

This function summarize the cross-section regression result at each time.

Package needed: prettytable.

Example

# continue the previous code
model.summary_by_time()
==========================================================================
+--------+-----------------+----------+--------------+---------------+
|  Year  |      Param      | R Square | Adj R Square | Sample Number |
+--------+-----------------+----------+--------------+---------------+
| 2001.0 | [-0.499 -0.990] |   0.53   |     0.53     |      3000     |
| 2002.0 | [-0.524 -0.987] |   0.56   |     0.56     |      3000     |
| 2003.0 | [-0.544 -1.015] |   0.58   |     0.58     |      3000     |
| 2004.0 | [-0.474 -0.948] |   0.53   |     0.53     |      3000     |
| 2005.0 | [-0.502 -1.007] |   0.57   |     0.57     |      3000     |
| 2006.0 | [-0.497 -0.981] |   0.55   |     0.55     |      3000     |
| 2007.0 | [-0.526 -1.020] |   0.57   |     0.57     |      3000     |
| 2008.0 | [-0.476 -1.024] |   0.56   |     0.56     |      3000     |
| 2009.0 | [-0.533 -1.011] |   0.57   |     0.57     |      3000     |
| 2010.0 | [-0.493 -1.029] |   0.57   |     0.57     |      3000     |
| 2011.0 | [-0.504 -0.975] |   0.55   |     0.55     |      3000     |
| 2012.0 | [-0.508 -1.002] |   0.56   |     0.56     |      3000     |
| 2013.0 | [-0.474 -1.015] |   0.56   |     0.56     |      3000     |
| 2014.0 | [-0.503 -0.998] |   0.55   |     0.55     |      3000     |
| 2015.0 | [-0.485 -1.034] |   0.55   |     0.55     |      3000     |
| 2016.0 | [-0.514 -1.005] |   0.57   |     0.57     |      3000     |
| 2017.0 | [-0.498 -1.016] |   0.58   |     0.58     |      3000     |
| 2018.0 | [-0.475 -0.994] |   0.55   |     0.55     |      3000     |
| 2019.0 | [-0.487 -0.974] |   0.54   |     0.54     |      3000     |
| 2020.0 | [-0.511 -1.031] |   0.56   |     0.56     |      3000     |
+--------+-----------------+----------+--------------+---------------+
def summary(self, charactername=None):

This function summarize the final result.

input :

charactername : The factors' name in the cross-section regression model.

Example

# continue the previous code
model.summary()
================================================================================
+-----------------+---------------------+-----------+---------------+-----------+
|      Param      |     Param Tvalue    | Average R | Average adj R | Average n |
+-----------------+---------------------+-----------+---------------+-----------+
| [-0.501 -1.003] | [-111.857 -202.247] |   0.558   |     0.558     |   3000.0  |
+-----------------+---------------------+-----------+---------------+-----------+

time_series_regress

class TS_regress()

This class is designed for time series regression, $$ r_{i,t} = \beta_if_t + \epsilon_{i,t} $$ to obtain the beta for each asset.

def _init_(self, list_y, factor):

This function initializes the object.

input :

list_y : The return matrix with i rows and t columns.

factor : The factor risk premium return series.

def ts_regress(self, newey_west=True):

This function is for conducting the time series regression.

input :

newey_west ： conduct the newey_west adjustment or not.

output :

self.alpha : The regression alpha.

self.e_mat : The error matrix

Example

from statsmodels.base.model import Model
from statsmodels.tools.tools import add_constant
from EAP.time_series_regress import TS_regress

X = np.random.normal(loc=0.0, scale=1.0, size=(2000,10))
y_list = []
for i in range(10) :
    b = np.random.uniform(low=0.1, high=1.1, size=(10,1))
    e = np.random.normal(loc=0.0, scale=1.0, size=(2000,1))
    y = X.dot(b) + e 
    y_list.append(y)

re = TS_regress(y_list, X)
def fit(self, **kwargs):

This function runs the function, ts_regress.

Example

# continue the previous code
re.fit()
def summary(self):

This function summarize the result, including the GRS test.

Example

# continue the previous code
re.summary()
=============================================================================
----------------------------------- GRS Test -------------------------------- 

GRS Statistics: 
 [[0.67160203]]
GRS p_value: 
 [[0.75175471]]
------------------------------------------------------------------------------
def grs(self):

This function conducts the GRS test.

output :

grs_stats : The GRS statistics.

p_value : The p_value.

Example

# continue the previous code
print(re.grs())
==============================================
(array([[0.67160203]]), array([[0.75175471]]))

cross_section_regress

class CS_regress()

def _init_(self, y_list, factor):

This function initializes the class.

input :

y_list : The assets return series list.

factor : The factor risk premium series.

def ts_regress(self):

This function conducts the time series regression.

output :

beta(N, c) : The betas for each asset.

err_mat : The error matrix.

def ave(self):

This function conducts the average operation on the assets returns series list.

output :

np.mean(self.y_list, axis=1) : The average of the assets returns series list.

def cs_regress(self, beta, err_mat, constant=True, gls=True, **kwargs):

This function takes the cross-sectional regression.

input :

beta : The betas from the output of the function ts_regress().

err_mat : The error matrix from the output of the function ts_regress().

constant : add constant or not. The default is add constant.

gls : GLS regression or OLS regression. The default is GLS regression.

output :

params : The params of the cross regression model.

resid : The residue of the cross regression model.

Example

from statsmodels.regression.linear_model import GLS
from EAP.cross_section_regress import CS_regress
import numpy as np
    
X = np.random.normal(loc=0, scale=0.1, size=(2000,3))
y_list = []
for i in range(100) :
    b = np.random.uniform(low=-1, high=1, size=(3,1))
    e = np.random.normal(loc=0.0, scale=0.5, size=(2000,1))
    alpha = np.random.normal(loc=0.0, scale=0.5)
    y = X.dot(b)  + e 
    y_list.append(y)
print(np.mean(X, axis= 0)) # average return of the factor risk premium 
========================================================================
[-0.00496423  0.00146649 -0.0004722 ]
def cov_mat(self, beta, err_mat, shanken=True, constant=True, gls=True, **kwargs):

This function calculates the covariance matrix of the cross regression model.

input :

beta : The betas from the output of the function ts_regress().

err_mat : The error matrix from the output of the function ts_regress().

shanken : Take the shanken adjustment or not. The default is True.

constant : add constant or not.

gls : GLS regression or OLS regression. The default is GLS regression.

output :

param_cov_mat : The covariance matrix of the parameters.

resid_cov_mat : The covariance matrix of the residue.

def t_test(self, param_cov_mat, params):

This function takes t-test for parameters.

input :

param_cov_mat : The covariance matrix of the parameters from the function cov_mat.

params : The parameters from the function cs_regress.

output :

t_value : The t-value for statistical inference.

p_value : The p-value for statistical inference.

def union_test(self, resid_cov_mat, resid):

This function takes union test for parameters.

input :

resid_cov_mat : The covariance matrix of the residue.

resid : The residue from the function cs_regress.

output :

chi_square : The chi-square statistics.

p_value : The p-value corresponding to the chi-square.

def fit(self, **kwargs):

This function runs the cross-sectional regression and takes the statistical inference.

def summary(self):

This function print the summary.

Example

# continue the previous code
print("\n---------------------GLS: Constant=True shanken=True------------------------\n")
re = CS_regress(y_list, X)
re.fit()
re.summary()
print("\n------------------------------------------------------------------------\n")
    
print("\n---------------------GLS: Constant=False shanken=True------------------------\n")
re = CS_regress(y_list, X)
re.fit(constant=False)
re.summary()
print("\n------------------------------------------------------------------------\n")
    
print("\n---------------------GLS: Constant=True shanken=False------------------------\n")
re = CS_regress(y_list, X)
re.fit(shanken=False)
re.summary()
print("\n------------------------------------------------------------------------\n")
    
print("\n---------------------GLS: Constant=False shanken=False------------------------\n")
re = CS_regress(y_list, X)
re.fit(constant=False, shanken=False)
re.summary()
print("\n------------------------------------------------------------------------\n")
    
print("\n---------------------OLS: Constant=True shanken=True------------------------\n")
re = CS_regress(y_list, X)
re.fit(gls=False)
re.summary()
print("\n------------------------------------------------------------------------\n")
    
print("\n---------------------OLS: Constant=False shanken=True------------------------\n")
re = CS_regress(y_list, X)
re.fit(constant=False, gls=False)
re.summary()
print("\n------------------------------------------------------------------------\n")
    
print("\n---------------------OLS: Constant=True shanken=False------------------------\n")
re = CS_regress(y_list, X)
re.fit(shanken=False, gls=False)
re.summary()
print("\n------------------------------------------------------------------------\n")
    
print("\n---------------------OLS: Constant=False shanken=False------------------------\n")
re = CS_regress(y_list, X)
re.fit(constant=False, shanken=False, gls=False)
re.summary()
print("\n------------------------------------------------------------------------\n")
================================================================================================================================
---------------------GLS: Constant=True shanken=True------------------------


-------------------------- Risk Premium ------------------------------

+-----------------------+---------------+--------------+
|         params        |    t_value    |   p_value    |
+-----------------------+---------------+--------------+
| -0.004239493082637248 | [-1.49931456] | [0.13394995] |
| 0.0018754489425203834 |  [0.64798047] |  [0.517072]  |
| -0.002623980021497935 | [-0.92194337] | [0.35666937] |
+-----------------------+---------------+--------------+

----------------------------------------------------------------------


----------------------------- Alpha test -----------------------------

+-----------------+----------------+
|    chi-square   |    p_value     |
+-----------------+----------------+
| [[89.27084753]] | [[0.69922497]] |
+-----------------+----------------+

----------------------------------------------------------------------


------------------------------------------------------------------------


---------------------GLS: Constant=False shanken=True------------------------


-------------------------- Risk Premium ------------------------------

+------------------------+---------------+--------------+
|         params         |    t_value    |   p_value    |
+------------------------+---------------+--------------+
| -0.0044337140100835495 | [-1.56801135] | [0.11703675] |
| 0.0014489988306153607  |  [0.50064261] | [0.61667778] |
| -0.0025199902303684996 |  [-0.8854116] | [0.37604117] |
+------------------------+---------------+--------------+

----------------------------------------------------------------------


----------------------------- Alpha test -----------------------------

+------------------+----------------+
|    chi-square    |    p_value     |
+------------------+----------------+
| [[123.73200185]] | [[0.03486519]] |
+------------------+----------------+

----------------------------------------------------------------------


------------------------------------------------------------------------


---------------------GLS: Constant=True shanken=False------------------------


-------------------------- Risk Premium ------------------------------

+-----------------------+---------------+--------------+
|         params        |    t_value    |   p_value    |
+-----------------------+---------------+--------------+
| -0.004239493082637248 | [-1.50013478] | [0.13373741] |
| 0.0018754489425203834 |  [0.64838824] | [0.51680835] |
| -0.002623980021497935 | [-0.92243422] | [0.35641345] |
+-----------------------+---------------+--------------+

----------------------------------------------------------------------


----------------------------- Alpha test -----------------------------

+-----------------+---------+
|    chi-square   | p_value |
+-----------------+---------+
| [[32.53458229]] |  [[1.]] |
+-----------------+---------+

----------------------------------------------------------------------


------------------------------------------------------------------------


---------------------GLS: Constant=False shanken=False------------------------


-------------------------- Risk Premium ------------------------------

+------------------------+---------------+--------------+
|         params         |    t_value    |   p_value    |
+------------------------+---------------+--------------+
| -0.0044337140100835495 | [-1.56885941] | [0.11683897] |
| 0.0014489988306153607  |  [0.50095408] | [0.6164586]  |
| -0.0025199902303684996 | [-0.88587763] | [0.37579002] |
+------------------------+---------------+--------------+

----------------------------------------------------------------------


----------------------------- Alpha test -----------------------------

+------------------+---------+
|    chi-square    | p_value |
+------------------+---------+
| [[-49.33885529]] |  [[1.]] |
+------------------+---------+

----------------------------------------------------------------------


------------------------------------------------------------------------


---------------------OLS: Constant=True shanken=True------------------------


-------------------------- Risk Premium ------------------------------

+------------------------+---------------+--------------+
|         params         |    t_value    |   p_value    |
+------------------------+---------------+--------------+
| -0.004191679829911098  | [-1.46410802] | [0.14332167] |
| 0.0026957168215120215  |  [0.91917806] | [0.35811334] |
| -0.0028054613152236852 |  [-0.9776489] | [0.3283663]  |
+------------------------+---------------+--------------+

----------------------------------------------------------------------


----------------------------- Alpha test -----------------------------

+------------------+----------------+
|    chi-square    |    p_value     |
+------------------+----------------+
| [[105.04417306]] | [[0.27097431]] |
+------------------+----------------+

----------------------------------------------------------------------


------------------------------------------------------------------------


---------------------OLS: Constant=False shanken=True------------------------


-------------------------- Risk Premium ------------------------------

+-----------------------+---------------+--------------+
|         params        |    t_value    |   p_value    |
+-----------------------+---------------+--------------+
| -0.004314458572417905 | [-1.50700942] | [0.13196625] |
|  0.002435573118655651 |  [0.83048514] | [0.40636372] |
| -0.002772551881136359 | [-0.96619054] | [0.33406572] |
+-----------------------+---------------+--------------+

----------------------------------------------------------------------


----------------------------- Alpha test -----------------------------

+------------------+----------------+
|    chi-square    |    p_value     |
+------------------+----------------+
| [[117.95438501]] | [[0.07282442]] |
+------------------+----------------+

----------------------------------------------------------------------


------------------------------------------------------------------------


---------------------OLS: Constant=True shanken=False------------------------


-------------------------- Risk Premium ------------------------------

+------------------------+---------------+--------------+
|         params         |    t_value    |   p_value    |
+------------------------+---------------+--------------+
| -0.004191679829911098  | [-1.46507223] | [0.14305847] |
| 0.0026957168215120215  |  [0.91987006] | [0.35775165] |
| -0.0028054613152236852 |  [-0.9782681] | [0.32806011] |
+------------------------+---------------+--------------+

----------------------------------------------------------------------


----------------------------- Alpha test -----------------------------

+------------------+---------------+
|    chi-square    |    p_value    |
+------------------+---------------+
| [[144.80511192]] | [[0.0011985]] |
+------------------+---------------+

----------------------------------------------------------------------


------------------------------------------------------------------------


---------------------OLS: Constant=False shanken=False------------------------


-------------------------- Risk Premium ------------------------------

+-----------------------+---------------+--------------+
|         params        |    t_value    |   p_value    |
+-----------------------+---------------+--------------+
| -0.004314458572417905 | [-1.50798575] | [0.13171619] |
|  0.002435573118655651 |  [0.8311002]  | [0.40601628] |
| -0.002772551881136359 | [-0.96679254] | [0.3337647]  |
+-----------------------+---------------+--------------+

----------------------------------------------------------------------


----------------------------- Alpha test -----------------------------

+------------------+----------------+
|    chi-square    |    p_value     |
+------------------+----------------+
| [[100.02211446]] | [[0.39645777]] |
+------------------+----------------+

----------------------------------------------------------------------


------------------------------------------------------------------------

adjust

This module consists of several common adjustment method in factor analysis.

def ols(y, x, constant=True):

The function is for OLS regression, which is equal to the OLS module in package statsmodels.

input :

y : The dependent variable.

x : The explanatory variable.

constant : add constant or not in OLS model. The default is True.

output :

result : The result of the regression.

import numpy as np
from statsmodels.base.model import Model
from statsmodels.tools.tools import add_constant
from EAP.adjust import newey_west, newey_west_t, ols, white_t
from EAP.adjust import white

X = np.random.normal(loc=0.0, scale=1.0, size=(2000,10))
b = np.random.uniform(low=0.1, high=1.1, size=(10,1))
e = np.random.normal(loc=0.0, scale=1.0, size=(2000,1))
y = X.dot(b) + e + 1.0

re = ols(y, X, constant=True)
print('\nTrue b : ', b)
print('\nEstimated b : ', re.params)
print('\nresidue : ', re.resid.shape)
====================================================
True b :  [[0.59169091]
 [0.91342353]
 [0.19599503]
 [0.9112773 ]
 [0.70647024]
 [0.41873624]
 [0.64871071]
 [0.20685505]
 [0.13172035]
 [0.82358063]]

Estimated b :  [1.00206596 0.57602159 0.91832825 0.2104454  0.935377   0.71526534
 0.39181771 0.65432445 0.22666925 0.13173488 0.83208811]

residue :  (2000,)
def white(y, X, **kwargs):

This function is for the White test. White estimate of variance:

X(r,c): r is sample number, c is variable number, S0 is covariance matrix of residue.

The variance estimate is $$ V_{ols}=T(X^X)^{-1}S_0(X^X)^{-1}. $$ The white estimation of S0 is $$ S_0=\frac 1T X^`(XR). $$ input :

y : The dependent variable.

X : The explanatory variable.

output :

V_ols : The white variance estimate

Example

# continue the previous code
import numpy as np
from statsmodels.api import add_constant

X = np.random.normal(loc=0.0, scale=1.0, size=(2000,10))
b = np.random.uniform(low=0.1, high=1.1, size=(10,1))
e = np.random.normal(loc=0.0, scale=1.0, size=(2000,1))
y = X.dot(b) + e + 1.0

re = white(y, X, constant=True)
np.set_printoptions(formatter={'float':'{:0.3f}'.format})
print(re*100)
X = add_constant(X)
r, c = np.shape(X)
print('\n', 1/r*X.T.dot(X).dot(re).dot(X.T.dot(X)))
============================================================================
[[0.052 0.004 0.002 0.002 0.000 -0.002 0.002 -0.004 -0.001 0.000 0.003]
 [0.004 0.056 0.002 -0.002 -0.003 -0.004 -0.001 -0.001 -0.003 0.004 0.001]
 [0.002 0.002 0.049 -0.003 -0.003 0.003 0.000 -0.002 -0.002 -0.003 0.002]
 [0.002 -0.002 -0.003 0.051 -0.002 -0.002 0.004 -0.000 -0.000 -0.001 0.002]
 [0.000 -0.003 -0.003 -0.002 0.054 0.004 0.000 -0.001 0.000 -0.001 0.003]
 [-0.002 -0.004 0.003 -0.002 0.004 0.055 -0.001 0.000 0.000 -0.002 0.001]
 [0.002 -0.001 0.000 0.004 0.000 -0.001 0.053 -0.003 -0.005 -0.002 0.004]
 [-0.004 -0.001 -0.002 -0.000 -0.001 0.000 -0.003 0.057 -0.001 -0.001 -0.002]
 [-0.001 -0.003 -0.002 -0.000 0.000 0.000 -0.005 -0.001 0.051 0.003 0.000]
 [0.000 0.004 -0.003 -0.001 -0.001 -0.002 -0.002 -0.001 0.003 0.049 0.002]
 [0.003 0.001 0.002 0.002 0.003 0.001 0.004 -0.002 0.000 0.002 0.052]]

 [[1.036 0.029 -0.028 0.031 0.007 -0.067 -0.004 0.003 0.029 -0.022 -0.041]
 [0.029 1.001 0.020 -0.056 -0.066 -0.023 0.000 -0.010 -0.070 0.069 0.023]
 [-0.028 0.020 0.972 -0.057 -0.019 0.058 -0.048 -0.002 0.084 -0.005 0.045]
 [0.031 -0.056 -0.057 1.004 -0.004 0.017 0.017 -0.072 -0.008 -0.042 0.041]
 [0.007 -0.066 -0.019 -0.004 1.024 0.045 -0.035 0.017 0.003 0.006 0.029]
 [-0.067 -0.023 0.058 0.017 0.045 1.125 0.010 -0.014 0.037 0.053 -0.017]
 [-0.004 0.000 -0.048 0.017 -0.035 0.010 1.053 -0.022 -0.047 0.047 0.035]
 [0.003 -0.010 -0.002 -0.072 0.017 -0.014 -0.022 0.955 -0.007 -0.002 -0.019]
 [0.029 -0.070 0.084 -0.008 0.003 0.037 -0.047 -0.007 1.008 -0.025 0.025]
 [-0.022 0.069 -0.005 -0.042 0.006 0.053 0.047 -0.002 -0.025 1.010 0.026]
 [-0.041 0.023 0.045 0.041 0.029 -0.017 0.035 -0.019 0.025 0.026 1.058]]
def newey_west(y, X, J=None):

This function is for Newey-West adjustment. Newey-West estimate of variance:

X(r,c): r is sample number, c is variable number, and S0 is covariance matrix of residue.

The estimate variance is $$ V_{ols}=T(X^X)^{-1}S_0(X^X)^{-1}. $$ The Newey-West estimate variance of S0 is $$ S_0= \frac1T X^(XR)+\frac1T \sum_j\sum_tw_je_te_{t-j}(X_tX^{t-j}+X{t-j}X^`_t). $$ input :

y : The dependent variable.

X : The explanatory variable.

J : The lag.

output :

V_ols : The Newey-West variance estimate.

Example

# continue the previous code
import numpy as np
from statsmodels.stats.sandwich_covariance import cov_hac

X = np.random.normal(loc=0.0, scale=1.0, size=(10000,10))
b = np.random.uniform(low=0.1, high=1.1, size=(10,1))
e = np.random.normal(loc=0.0, scale=1.0, size=(10000,1))
y = X.dot(b) + e + 1.0

re = newey_west(y, X, constant=False)
np.set_printoptions(formatter={'float':'{:0.2f}'.format})
print(re)
# X = add_constant(X)
r, c = np.shape(X) 
print('\n', 1/r*X.T.dot(X).dot(re).dot(X.T.dot(X)))
result = ols(y, X, constant=False)
print('\n', cov_hac(result))
print('\n', 1/r*X.T.dot(X).dot(cov_hac(result)).dot(X.T.dot(X)))
========================================================================
[[0.00 -0.00 -0.00 0.00 0.00 0.00 -0.00 0.00 -0.00 -0.00]
 [-0.00 0.00 -0.00 -0.00 -0.00 0.00 -0.00 -0.00 0.00 -0.00]
 [-0.00 -0.00 0.00 -0.00 -0.00 -0.00 -0.00 -0.00 -0.00 0.00]
 [0.00 -0.00 -0.00 0.00 -0.00 -0.00 -0.00 0.00 -0.00 -0.00]
 [0.00 -0.00 -0.00 -0.00 0.00 0.00 -0.00 -0.00 0.00 0.00]
 [0.00 0.00 -0.00 -0.00 0.00 0.00 -0.00 -0.00 -0.00 0.00]
 [-0.00 -0.00 -0.00 -0.00 -0.00 -0.00 0.00 0.00 0.00 0.00]
 [0.00 -0.00 -0.00 0.00 -0.00 -0.00 0.00 0.00 -0.00 -0.00]
 [-0.00 0.00 -0.00 -0.00 0.00 -0.00 0.00 -0.00 0.00 0.00]
 [-0.00 -0.00 0.00 -0.00 0.00 0.00 0.00 -0.00 0.00 0.00]]

 [[2.08 0.00 -0.09 -0.01 -0.03 -0.05 -0.02 0.00 -0.02 0.01]
 [0.00 2.01 0.04 -0.00 0.00 -0.03 -0.00 -0.01 -0.00 0.02]
 [-0.09 0.04 1.99 -0.02 0.01 0.00 -0.01 -0.08 0.03 0.02]
 [-0.01 -0.00 -0.02 1.96 -0.00 -0.05 -0.01 -0.04 -0.01 -0.02]
 [-0.03 0.00 0.01 -0.00 1.98 0.06 0.00 0.04 -0.01 -0.05]
 [-0.05 -0.03 0.00 -0.05 0.06 1.94 -0.01 -0.00 -0.01 -0.02]
 [-0.02 -0.00 -0.01 -0.01 0.00 -0.01 2.04 -0.00 0.01 -0.07]
 [0.00 -0.01 -0.08 -0.04 0.04 -0.00 -0.00 1.89 -0.05 -0.02]
 [-0.02 -0.00 0.03 -0.01 -0.01 -0.01 0.01 -0.05 1.97 -0.01]
 [0.01 0.02 0.02 -0.02 -0.05 -0.02 -0.07 -0.02 -0.01 1.93]]

 [[0.00 -0.00 0.00 0.00 0.00 0.00 -0.00 0.00 0.00 -0.00]
 [-0.00 0.00 0.00 -0.00 0.00 0.00 -0.00 0.00 -0.00 -0.00]
 [0.00 0.00 0.00 -0.00 -0.00 0.00 -0.00 -0.00 -0.00 0.00]
 [0.00 -0.00 -0.00 0.00 0.00 -0.00 -0.00 -0.00 -0.00 -0.00]
 [0.00 0.00 -0.00 0.00 0.00 0.00 0.00 -0.00 0.00 0.00]
 [0.00 0.00 0.00 -0.00 0.00 0.00 -0.00 -0.00 -0.00 -0.00]
 [-0.00 -0.00 -0.00 -0.00 0.00 -0.00 0.00 0.00 -0.00 0.00]
 [0.00 0.00 -0.00 -0.00 -0.00 -0.00 0.00 0.00 -0.00 0.00]
 [0.00 -0.00 -0.00 -0.00 0.00 -0.00 -0.00 -0.00 0.00 0.00]
 [-0.00 -0.00 0.00 -0.00 0.00 -0.00 0.00 0.00 0.00 0.00]]

 [[2.07 -0.05 -0.04 0.02 0.06 -0.11 -0.08 0.03 0.05 0.02]
 [-0.05 1.91 0.10 0.01 0.07 0.00 0.01 0.02 -0.09 0.03]
 [-0.04 0.10 2.05 -0.06 0.01 0.07 -0.06 -0.11 -0.15 0.04]
 [0.02 0.01 -0.06 1.87 0.04 -0.05 -0.02 -0.10 -0.01 -0.06]
 [0.06 0.07 0.01 0.04 2.00 0.11 0.05 0.03 -0.00 -0.04]
 [-0.11 0.00 0.07 -0.05 0.11 1.91 0.00 -0.05 -0.05 -0.05]
 [-0.08 0.01 -0.06 -0.02 0.05 0.00 1.99 0.03 -0.02 -0.10]
 [0.03 0.02 -0.11 -0.10 0.03 -0.05 0.03 2.01 -0.10 0.06]
 [0.05 -0.09 -0.15 -0.01 -0.00 -0.05 -0.02 -0.10 2.16 0.01]
 [0.02 0.03 0.04 -0.06 -0.04 -0.05 -0.10 0.06 0.01 1.97]]
def white_t(y, X, params=None, **kwargs):

This function constructs t-test based on White variance estimate.

input :

y : The dependent variable.

X : The explanatory variable.

params : Already have parameters or not. The default is None.

output :

t_value : The t-value of parameters.

p_value : The p-value of parameters.

Example

import numpy as np

X = np.random.normal(loc=0.0, scale=1.0, size=(10000,10))
b = np.random.uniform(low=-0.5, high=0.5, size=(10,1))
e = np.random.normal(loc=0.0, scale=1.0, size=(10000,1))
y = X.dot(b) + e + 1.0

re = white_t(y, X, constant=False)
np.set_printoptions(formatter={'float':'{:0.2f}'.format})
print('t_value : ', re[0], '\np_value : ', re[1])
print('b :', b.T)
=========================================================================
t_value :  [2.50 34.58 13.23 6.56 -17.64 -34.69 -16.40 13.84 28.90 30.64] 
p_value :  [0.01 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00]
b : [[0.02 0.49 0.18 0.09 -0.25 -0.49 -0.22 0.19 0.44 0.43]]
def newey_west_t(y, X, params=None):

This function constructs t-test based on Newey-West variance estimate.

input :

y : The dependent variable.

X : The explanatory variable.

params : Already have parameters or not. The default is None.

output :

t_value : The t-value of parameters.

p_value : The p-value of parameters.

Example

import numpy as np

X = np.random.normal(loc=0.0, scale=1.0, size=(10000,10))
b = np.random.uniform(low=-0.5, high=0.5, size=(10,1))
e = np.random.normal(loc=0.0, scale=1.0, size=(10000,1))
y = X.dot(b) + e + 1.0

re = newey_west_t(y, X, constant=True)
np.set_printoptions(formatter={'float':'{:0.2f}'.format})
print('t_value : ', re[0], '\np_value : ', re[1])
print('b :', b.T)
=================================================================================
t_value :  [135.08 -17.19 13.80 34.95 14.61 21.31 48.56 -44.62 2.75 -28.71 51.63] 
p_value :  [0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00]
b : [[-0.14 0.10 0.25 0.11 0.16 0.40 -0.36 0.03 -0.21 0.40]]

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